AI knowledge both concentrates and disperses: moderate local stickiness channels AI activity into narrower sub-technology branches, but beyond a threshold stickiness promotes dispersion; complexity reshapes the curve, and the inverted-U is clearest in eastern and smaller Chinese cities.

Main Finding

Using a city-year panel of Chinese AI patenting (2014–2023) and two-way fixed-effects regressions, the authors find an inverted U‑shaped association between city-level AI knowledge stickiness and technological concentration (measured by HHI over AI sub-technology branches). Moderate stickiness increases local technological concentration (supporting cumulative local learning), but beyond a turning point higher stickiness reduces concentration (consistent with lock‑in and weakened renewal). Technological complexity moderates this nonlinear relationship by changing its strength and curvature. The inverted U pattern is clearest in eastern and in small/medium cities; evidence is weaker for large cities where the quadratic term is not significant.

Key Points

• Conceptualization: Knowledge stickiness is framed as a two‑dimensional system balancing diffusion potential and resistance/lock‑in (rather than a single proxy).
• Empirical pattern: An inverted U (β1>0, β2<0) links stickiness to technological concentration — i.e., some stickiness fosters specialization, too much produces lock‑in and dispersion across subfields.
• Moderation by complexity: Technological complexity does not simply shift the turning point uniformly; it alters the magnitude and curvature of the inverted U, intensifying the positive effect at low-to-moderate stickiness and strengthening the negative effect beyond the peak.
• Heterogeneity: The nonlinear relationship is more pronounced in eastern cities and in small/medium cities. Large cities show weaker evidence for the quadratic effect, consistent with greater absorptive capacity and external network mitigation of lock‑in.
• Interpretation: Results are reported as conditional associations (not causal estimates).

Data & Methods

• Data: City-level AI patent applications combined with urban statistics for Chinese cities, panel 2014–2023. AI sub-technology branches follow the 2023 Classification System for Patents of Key Digital Technologies.
• Dependent variable: Technological concentration measured by Herfindahl–Hirschman Index (HHI) of a city’s AI patents across mapped sub-technology branches.
• Main independent variable: Knowledge stickiness operationalized via a two‑dimensional indicator system:
  • Diffusion (higher → more fluid knowledge): average patent citations, IPC classification entropy (technical variety), share of collaborative patents.
  • Resistance/lock‑in (higher → more closure): share of sole applicants, concentration of “hot” technologies, within‑city patent concentration.
  • (The paper constructs a composite measure capturing the balance between diffusion and resistance—details of weighting/aggregation are in the full methods section.)
• Moderator: Technological complexity of the local AI knowledge base (measured using knowledge‑relatedness/complexity metrics derived from patent classifications; exact operationalization in paper).
• Estimation: Two‑way fixed effects panel regressions (city and year fixed effects) that include the quadratic term of stickiness to capture nonlinearity and interaction terms (stickiness × complexity) to test moderation. Robustness and subgroup analyses (region, city size) were performed.
• Controls: Urban covariates (standard controls like city GDP, population, R&D inputs, industrial structure) are included (see full paper for list).
• Caveats: Paper is an unedited in‑press manuscript; results are associational and rely on patent measures and chosen classification system.

Implications for AI Economics

• Nonlinear agglomeration dynamics: Policy and models of AI diffusion should account for nonlinearity—moderate local embedding of AI knowledge supports specialization, but excessive localization produces lock‑in that undermines sustained concentration.
• Complexity matters: The role of knowledge complexity as a moderator implies that sectors/subfields with higher technical complexity need different place‑based strategies (stronger local complementarities and coordination) than less complex subfields.
• Place‑based policy design: Policymakers should aim for “embedded openness” — encourage local capability accumulation while preserving channels for external knowledge inflows (collaborative projects, mobility, cross‑city partnerships) to avoid lock‑in.
• Targeted support for lagging cities: Small/medium and inland cities hit the declining side of the curve earlier; these places need policies to reduce resistance (e.g., incentives for collaborative patents, talent exchange, data‑sharing platforms) and to broaden their sub-technology portfolios to prevent premature specialization traps.
• Monitoring and metrics: Using mapped sub-technology HHIs and stickiness indicators can help cities monitor whether they are on the rising or declining portion of the inverted U, informing interventions (e.g., diversify activities if near/after the peak).
• Research implications: Empirical work on AI agglomeration should model nonlinearities and interactions with complexity and account for heterogeneity across urban contexts. Patent‑based mapping at sub‑technology resolution is a useful tool for that purpose.
• Caution on generalization: Results are China‑specific and patent‑based; applicability to other countries or to non‑patented AI activity (open‑source, models) requires further work.